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Question: The value of \(\sum_{k = 1}^{6}\left( \sin\frac{2\pi k}{7} - i\cos\frac{2\pi k}{7} \right)\) is –...

The value of ∑k=16(sin⁡2πk7−icos⁡2πk7)\sum_{k = 1}^{6}\left( \sin\frac{2\pi k}{7} - i\cos\frac{2\pi k}{7} \right) is –

A

0

B

– 1

C

I

D

– i

Answer

I

Explanation

Solution

Sol. ∑K=1n−1cos⁡2πKn=−1\sum_{K = 1}^{n - 1}{\cos\frac{2\pi K}{n} = - 1}